The storage within the phone is a SSD chip which is not user changeable.
You're only option here is to replace the logic board which gets tricky! You see, many are from stolen phones and are locked either by the carrier and/or by Apple so you end up loosing your money to a crook. Basically, it's not worth the costs and risks upgrading the phone.
I would wait here as the next iOS will offer a smaller footprint and methods of shrinking the apps as well freeing up more space.
Look at iCloud if you don't have it as well as look at an external SSD drive which allows you to download some of your pictures (or other stuff) if you are traveling.